Mr Biden’s comments were made at an informal Democratic Party fundraising dinner at a private residence in Los Angeles on Thursday.
Speaking about China and its leader Xi Jinping, he pondered the US’s role in relation to China as it grapples with its positions on Russia, India and Pakistan.
“How do we handle that?” Mr Biden said, according to a transcript posted on the White House website. “How do we handle that relative to what’s going on in Russia? And what I think is maybe one of the most dangerous nations in the world: Pakistan. Nuclear weapons without any cohesion.”
Mr Bhutto Zardari said he was surprised by the comments. “As far as the question of the safety and security of Pakistan's nuclear assets are concerned, we meet all — each and every — international standard in accordance with the IAEA,” he said at a press conference on Saturday.
The foreign minister said he did not think the decision to summon the US ambassador would negatively affect relations with the United States.
“Pakistan’s disappointment and concern was conveyed to the US envoy on the unwarranted remarks, which were not based on ground reality or facts,” the Ministry of Foreign Affairs said.
Mr Bhutto Zardari said worries about Pakistan's nuclear programme were not raised on his recent trip to Washington, where he held extensive meetings, including at the State Department.
Ties between Islamabad and Washington, once close allies, have started to warm after years of frosty relations, mostly due to concerns about Pakistan's alleged support of the Taliban in Afghanistan. Pakistan denies this support.
Pakistani Prime Minister Shehbaz Sharif said Mr Biden’s comments were factually incorrect and misleading.
Pakistan over the years has proved itself to be a responsible nuclear state, and its nuclear programme is managed through a technically sound command and control system, Mr Sharif said in a statement.
He pointed to Pakistan’s commitment to global standards including those of the International Atomic Energy Agency.
Mr Bhutto Zardari said earlier in Karachi that he believed it was the sort of misunderstanding that was created when there was a lack of engagement, apparently referring to the government of former prime minister Imran Khan.
“When Pakistan has nuclear assets we know how to keep them safe and secure, how to protect them as well,” he said.
He said that if there was any question about nuclear weapons security in the region, it should be raised with Pakistan’s nuclear-armed neighbour, India. He said India recently fired a missile that landed accidentally in Pakistan.
Pakistan and India have been arch-rivals since their independence from British rule in 1947. They have bitter relations over the disputed Himalayan region of Kashmir, which is divided between them and claimed by both in its entirety. They fought two of their three wars over Kashmir.
— With reporting from AP and Reuters.